




from math import pi, sqrt, tan



def 				_A  (		lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if side_length < 0:
          raise ValueError("surface_area_cube() only accepts non-negative values"     )
     return 6 * side_length**2



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if length < 0 or breadth < 0 or height < 0:
          raise ValueError("surface_area_cuboid() only accepts non-negative values"     )
     return 2 * ((length * breadth) + (breadth * height) + (length * height))



def 				_A  (		lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if radius < 0:
          raise ValueError("surface_area_sphere() only accepts non-negative values"     )
     return 4 * pi * radius**2



def 				_A  (		lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if radius < 0:
          raise ValueError("surface_area_hemisphere() only accepts non-negative values"     )
     return 3 * pi * radius**2



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if radius < 0 or height < 0:
          raise ValueError("surface_area_cone() only accepts non-negative values"     )
     return pi * radius * (radius + (height**2 + radius**2) ** 0.5)



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if radius_a < 0 or radius_a < 0 or height < 0:
          raise ValueError(
              "surface_area_conical_frustum() only accepts non-negative values"     )
     lowerCAmelCase__            =					(height**2 + (radius_a - radius_a) ** 2) ** 0.5
     return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if radius < 0 or height < 0:
          raise ValueError("surface_area_cylinder() only accepts non-negative values"     )
     return 2 * pi * radius * (height + radius)



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if torus_radius < 0 or tube_radius < 0:
          raise ValueError("surface_area_torus() only accepts non-negative values"     )
     if torus_radius < tube_radius:
          raise ValueError(
              "surface_area_torus() does not support spindle or self intersecting tori"     )
     return 4 * pow(lowerCAmelCase_  ,							2     ) * torus_radius * tube_radius



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if length < 0 or width < 0:
          raise ValueError("area_rectangle() only accepts non-negative values"     )
     return length * width



def 				_A  (		lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if side_length < 0:
          raise ValueError("area_square() only accepts non-negative values"     )
     return side_length**2



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if base < 0 or height < 0:
          raise ValueError("area_triangle() only accepts non-negative values"     )
     return (base * height) / 2



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if sidea < 0 or sidea < 0 or sidea < 0:
          raise ValueError("area_triangle_three_sides() only accepts non-negative values"     )
     elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
          raise ValueError("Given three sides do not form a triangle"     )
     lowerCAmelCase__            =					(sidea + sidea + sidea) / 2
     lowerCAmelCase__            =					sqrt(
         semi_perimeter
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)     )
     return area



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if base < 0 or height < 0:
          raise ValueError("area_parallelogram() only accepts non-negative values"     )
     return base * height



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if basea < 0 or basea < 0 or height < 0:
          raise ValueError("area_trapezium() only accepts non-negative values"     )
     return 1 / 2 * (basea + basea) * height



def 				_A  (		lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if radius < 0:
          raise ValueError("area_circle() only accepts non-negative values"     )
     return pi * radius**2



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if radius_x < 0 or radius_y < 0:
          raise ValueError("area_ellipse() only accepts non-negative values"     )
     return pi * radius_x * radius_y



def 				_A  (		lowerCAmelCase_	:   float  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if diagonal_a < 0 or diagonal_a < 0:
          raise ValueError("area_rhombus() only accepts non-negative values"     )
     return 1 / 2 * diagonal_a * diagonal_a



def 				_A  (		lowerCAmelCase_	:   int  ,							lowerCAmelCase_	:   float     ):
     """simple docstring"""

     if not isinstance(lowerCAmelCase_  ,							lowerCAmelCase_     ) or sides < 3:
          raise ValueError(
              "area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides"     )
     elif length < 0:
          raise ValueError(
              "area_reg_polygon() only accepts non-negative values as \
length of a side"     )
     return (sides * length**2) / (4 * tan(pi / sides     ))
     return (sides * length**2) / (4 * tan(pi / sides     ))


if __name__ == "__main__":
     import doctest

     doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

     print('[DEMO] Areas of various geometric shapes: \n')
     print(F"""Rectangle: {area_rectangle(10, 20) = }""")
     print(F"""Square: {area_square(10) = }""")
     print(F"""Triangle: {area_triangle(10, 10) = }""")
     print(F"""Triangle: {area_triangle_three_sides(5, 12, 13) = }""")
     print(F"""Parallelogram: {area_parallelogram(10, 20) = }""")
     print(F"""Rhombus: {area_rhombus(10, 20) = }""")
     print(F"""Trapezium: {area_trapezium(10, 20, 30) = }""")
     print(F"""Circle: {area_circle(20) = }""")
     print(F"""Ellipse: {area_ellipse(10, 20) = }""")
     print('\nSurface Areas of various geometric shapes: \n')
     print(F"""Cube: {surface_area_cube(20) = }""")
     print(F"""Cuboid: {surface_area_cuboid(10, 20, 30) = }""")
     print(F"""Sphere: {surface_area_sphere(20) = }""")
     print(F"""Hemisphere: {surface_area_hemisphere(20) = }""")
     print(F"""Cone: {surface_area_cone(10, 20) = }""")
     print(F"""Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }""")
     print(F"""Cylinder: {surface_area_cylinder(10, 20) = }""")
     print(F"""Torus: {surface_area_torus(20, 10) = }""")
     print(F"""Equilateral Triangle: {area_reg_polygon(3, 10) = }""")
     print(F"""Square: {area_reg_polygon(4, 10) = }""")
     print(F"""Reqular Pentagon: {area_reg_polygon(5, 10) = }""")

def 			lowercase(	UpperCamelCase_							,					UpperCamelCase_							,					UpperCamelCase_       )		->	list:







 '''simple docstring'''
 UpperCamelCase			  =      len(UpperCamelCase_       )
 UpperCamelCase			  =      [[0] * n for i in range(UpperCamelCase_       )]
 for i in range(UpperCamelCase_       ):
  UpperCamelCase			  =      y_points[i]

 for i in range(2							,					UpperCamelCase_       ):
  for j in range(UpperCamelCase_							,					UpperCamelCase_       ):
   UpperCamelCase			  =      (
       (xa - x_points[j - i + 1]) * q[j][i - 1]
       - (xa - x_points[j]) * q[j - 1][i - 1]
   ) / (x_points[j] - x_points[j - i + 1])

 return [q[n - 1][n - 1], q]


if __name__ == "__main__":
     import doctest

     doctest.testmod()
